Simplify the following expression: $k = \dfrac{x}{7} + \dfrac{x}{8}$
Answer: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $7$ and $8$ $\lcm(7, 8) = 56$ $ k = \dfrac{8}{8} \cdot \dfrac{x}{7} + \dfrac{7}{7} \cdot \dfrac{x}{8} $ $k = \dfrac{8x}{56} + \dfrac{7x}{56}$ $k = \dfrac{8x +7x}{56}$ $k = \dfrac{15x}{56}$